PPT-Cryptography Lecture 14 Other applications of

hash functions Hash functions are ubiquitous Collisionresistance fingerprinting Outsourced storage Used as a random oracle Used as a oneway function Password hashing Key . However computational aspects of lattices were not investigated much until the early 1980s when they were successfully employed for breaking several proposed cryptosystems among many other applications It was not until the late 1990s that lattices w Intro to IT. . COSC1078 Introduction to Information Technology. . Lecture 22. Internet Security. James Harland. james.harland@rmit.edu.au. Lecture 20: Internet. Intro to IT. . Introduction to IT. By . Abhijith. . Chandrashekar. . and . Dushyant. . Maheshwary. Introduction. What are Elliptic Curves?. Curve with standard form y. 2. = x. 3 . + ax + b a, b . ϵ ℝ. Characteristics of Elliptic Curve. CS 465. Last Updated. : . Aug 25, 2015. Outline. Provide a brief historical background of cryptography. Introduce definitions and high-level description of four cryptographic primitives we will learn about this semester. Sixth Edition. by William Stallings . Chapter 10. Other Public-Key Cryptosystems. “Amongst the tribes of Central Australia every man, woman, and child has a secret or sacred name which is bestowed by the older men upon him or her soon after birth, and which is known to none but the fully initiated members of the group. This secret name is never mentioned except upon the most solemn occasions; to utter it in the hearing of men of another group would be a most serious breach of tribal custom. When mentioned at all, the name is spoken only in a whisper, and not until the most elaborate precautions have been taken that it shall be heard by no one but members of the group. The native thinks that a stranger knowing his secret name would have special power to work him ill by means of magic.”. Algorithms. Scott Chappell. What is Cryptography?. Definition: the art of writing or solving codes. Basic Encryption Methods. Caesar Shift. Simple Substitution Cipher. Fun to use, but are easily cracked by computers and even by humans. CS. . 111. Operating . Systems . Peter Reiher. . Outline. Basic concepts in computer security. Design principles for security. Important security tools for operating systems. Access control. Cryptography and operating systems. Josh Benaloh. Tolga Acar. Fall 2016. November 8, 2016. Practical Aspects of Modern Cryptography. 1. What is Money?. 106 billion people lived. 94% are dead. Most of the world’s wealth made after 1800. 1. Part I: Crypto. Part 1 . . Cryptography . 2. Crypto. Cryptology . . The art and science of making and breaking “secret codes”. Richard J. Blech. Chief Executive Officer. Secure Channels, Inc.. Is there anyone here who cannot parse and explain this equation?. 2. If not, that’s ok.. 3. Why Pre-Computer Cryptography?. If you understand pre-computer crypto, you understand crypto!. Josh Benaloh. Tolga Acar. Fall 2016. October 25, 2016. 2. The wiretap channel. Key (K. 1. ). Key (K. 2. ). Eavesdropper. Plaintext. (P). Noisy insecure. channel. Encrypt. Decrypt. Alice. Bob. Plaintext. Steven M. Bellovin. https://www.cs.columbia.edu/~smb. What is Cryptography?. Literally: “hidden writing”. (Technical, the entire field is “cryptology”, but almost no one except the NSA and historians uses that word.). Cyclic group G of order q with generator g.  G.  . G = {g. 0. , g. 1. , …, g. q-1. }. For any h .  G, define . log. g. h .  {0, …, q-1} as. . log. g. h = x  . Crypto is amazing. Can do things that initially seem impossible. Crypto is important. It impacts each of us every day. Crypto is fun!. Deep theory. Attackers’ mindset. Necessary administrative stuff.